If `vec(A)=4hat(i)-3hat(j)` and `vec(B)=6hat(i)+8hat(j)`,then find the magnitude and direction of `vec(A)+vec(B)`.

Options

A. `5, tan^(-1)(3//4)`
B. `5 sqrt(5), tan^(-1)(1//2)`
C. `10, tan^(-1)(5)`
D. `25, tan^(-1)(3//4)`

Answer

B

Explanation

`vec(A)+vec(B)= 4hat(i)-3hat(j)+6hat(i)+8hat(j)= 10hat(i)+5hat(j)`
`|vec(A)+vec(B)|= sqrt((10)^(2)+(5)^(2))=5sqrt(5)`
`tan theta= 5/(10)= 1/2implies theta= tan^(-1)(1/2)`